### Problem Statement

I give my true love presents every day. On day 1, I give her one Type 1 present. On day 2, I give her two Type 2 presents, followed by one Type 1 present. On day 3, I give her three Type 3 presents, followed by two Type 2 presents, followed by one Type 1 present. This pattern continues day after day. Soon I begin to wonder, what type of present will be the 100th present that I give my true love? The 1000th? The 1000000th?

For example, the 10th present that I give my true love is the Type 1 present on day 3.

Write a method that takes an int n and returns the type of the nth present that I give my true love. Note that n is one-based, so n=1 refers to the very first present I give her (the Type 1 present on day 1).

### Definition

 Class: TwoTurtledoves Method: presentType Parameters: int Returns: int Method signature: int presentType(int n) (be sure your method is public)

### Notes

-Unlike the poseur in the popular Christmas song, I do not stop giving my true love presents after the 12th day.

### Constraints

-n is between 1 and 1000000000, inclusive.

### Examples

0)

 `10`
`Returns: 1`
 The example above.
1)

 `12`
`Returns: 4`
 The second of four Type 4 presents on Day 4.
2)

 `399`
`Returns: 11`
3)

 `123456`
`Returns: 65`
4)

 `1000000000`
`Returns: 1704`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=1948

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=5870&pm=1948

vorthys

#### Testers:

PabloGilberto , lbackstrom , brett1479

#### Problem categories:

Simple Search, Iteration